Showing papers on "Pairwise comparison published in 1990"
TL;DR: In this paper, the authors present a pairwise meetings model of trade where agents have asymmetric information about the true state of the world and the focus is on the transmission of the information through the process of trade.
Abstract: The paper presents a simple pairwise meetings model of trade. The new feature is that agents have asymmetric information about the true state of the world. The focus is on the transmission of the information through the process of trade. The qualitative question is : to what extent is the information revealed to uninformed agents through the trading process, when the market is in some sense frictionless? In particular ; does the decentralized process give rise to full revelation results as derived by the literature on rational expectations for centralized and competitive environments? In the context of the model of this paper, it turns out that the information is not fully revealed to uninformed agents, even when the market is in some sense approximately frictionless.
158 citations
TL;DR: This article proposed further opportunities for effort reduction through globally effective elicitation process and demonstrated impressive savings in the number of comparisons a decision maker is required to make when using the AHP for complex problems.
93 citations
TL;DR: In this paper, the authors report three medieval works, hitherto unknown to social choice, which discuss procedures for elections when there are more than two candidates and propose Borda methods and the third a Condorcet method of successive pairwise comparison.
Abstract: We report three medieval works, hitherto unknown to social choice, which discuss procedures for elections when there are more than two candidates. Two of the three propose Borda methods and the third a Condorcet method of successive pairwise comparison. All three discuss problems of manipulation. One of them displays a matrix for pairwise comparisons; this is a work written in 1299, nearly 600 years before the matrix notation was believed to have been invented by C. L. Dodgson. We conclude with a review of the theory of voting in medieval Europe.
91 citations
TL;DR: The main objective of the study was to experiment with multi-criteria analysis and to design a robust reallocation method, although there is no unique numerical scale to quantify verbal human judgement and no unique cost-benefit relationship.
87 citations
TL;DR: In this paper, a regime analysis method is proposed to find the best available compromise by identifying that option which ensures the highest score probability that is embodied in the ordinal information, based on the principle of insufficient reasoning and leading in general to an unambiguous choice.
Abstract: In recent years an avalanche of literature has been published in the field of multiple criteria analysis. This methodology for decision-making and evaluation serves to find the best compromise solutions among alternative choice options, taking into account the existence of conflicting judgment criteria. The present paper focuses attention on one particular class of multiple criteria methods, viz. those in which the available information (impacts and policy priorities) is measured in an ordinal sense. This low level of measurement precludes the application of standard numerical methods. For this problem a new method, the so-called regime analysis, is devised in the paper. This method is based on a pairwise comparison of choice options and serves to find the best available compromise by identifying that option which ensures the highest score probability that is embodied in the ordinal information. The formal derivation is based upon the principle of insufficient reasoning and leads in general to an unambiguous choice. Particular attention is also given to the existence of ties and of mixed (i.e. qualitative-quantitative) information. The method is illustrated by means of an evaluation problem regarding 12 types of automobiles on the basis of a variety of judgement criteria.
82 citations
TL;DR: A method for acceleration of simultaneous multiple sequence alignment is proposed in which consistent regions serve as "anchor points" limiting application of direct multi-way alignment to the rest of "inconsistent" regions.
77 citations
TL;DR: It will be proved that the only solution satisfying consistency axioms for the problem of retrieving weights from inconsistent additive judgements matrices is the arithmetic mean.
76 citations
TL;DR: There is a high potential for permanent genetic diversity in the pairwise interaction model, and insight is provided into the extent to which various forms of genotypic interactions enhance or reduce this potential.
Abstract: A detailed analytic and numerical study is made of the potential for permanent genetic variation in frequency-dependent models based on pairwise interactions among genotypes at a single diallelic locus. The full equilibrium structure and qualitative gene-frequency dynamics are derived analytically for a symmetric model, in which pairwise fitnesses are chiefly determined by the genetic similarity of the individuals involved. This is supplemented by an extensive numerical investigation of the general model, the symmetric model, and nine other special cases. Together the results show that there is a high potential for permanent genetic diversity in the pairwise interaction model, and provide insight into the extent to which various forms of genotypic interactions enhance or reduce this potential. Technically, although two stable polymorphic equilibria are possible, the increased likelihood of maintaining both alleles, and the poor performance of protected polymorphism conditions as a measure of this likelihood, are primarily due to a greater variety and frequency of equilibrium patterns with one stable polymorphic equilibrium, in conjunction with a disproportionately large domain of attraction for stable internal equilibria.
47 citations
01 Jan 1990
TL;DR: A method for consensus measuring in a group decision problem is presented for the multiple criteria case, which allows a fuzzy interpretation of the problem and the definition of a consensus measure by means of fuzzy tools as linguistic quantifiers.
Abstract: A method for consensus measuring in a group decision problem is presented for the multiple criteria case. The decision process is supposed to be carried out according to Saaty’s Analytic Hierarchy Process, and hence using pairwise comparison among the alternatives. Using a suitable distance between the experts’ judgements, a scale transformation is proposed which allows a fuzzy interpretation of the problem and the definition of a consensus measure by means of fuzzy tools as linguistic quantifiers. Sufficient conditions on the expert’s judgements are finally presented, which guarantee any a priori fixed consensus level to be reached.
40 citations
01 Jan 1990
TL;DR: The approach proposed may be considered as an attempt to make explicit the limited capacity of the human mind to make comparisons between numerous and often conflicting evaluations simultaneously; it offers a series of comparisons easy to execute one at a time.
Abstract: The aim of the two methods briefly outlined here is to aid the decision maker with discrete problems in the presence of more than one cardinal criterion. Methodologically the two have much in common with the original Pairwise Criterion Comparison Approach (PCCA) whose specific quality consists in the possibility to compare feasible actions with respect to all the possible unranked pairs of distinct criteria considered. The partial results thus obtained are then suitably aggregated and used in order to aid the decision maker in a variety of problems. From this point of view, therefore, the approach proposed may be considered as an attempt to make explicit the limited capacity of the human mind to make comparisons between numerous and often conflicting evaluations simultaneously; it offers, instead, a series of comparisons easy to execute one at a time.
25 citations
TL;DR: In this article, the authors address the problem of specifying differential weights for variables in the construction of a measure of dissimilarity, where an assessor is required to provide subjective judgments of the pairwise dissimilarities within a training set of objects, and these differences are then modeled as a function of the recorded differences between the objects on each of the variables.
Abstract: The paper addresses the problem of specifying differential weights for variables in the construction of a measure of dissimilarity. An assessor is required to provide subjective judgments of the pairwise dissimilarities within a training set of objects, and these dissimilarities are then modeled as a function of the recorded differences between the objects on each of the variables. The aim is to make explicit the relative importance that assessors attach to each of the variables, and thus obtain guidance on how these variables should be combined into a relevant dissimilarity matrix. The methodology is illustrated by application to some archaeological data.
Journal Article•
TL;DR: With all the multiple comparison tests cited above, the logical question is, "Which procedure is best?"
Abstract: With all the multiple comparison tests cited above, the logical question is, "Which procedure is best?" The answer to this question depends on whether an individual's decisions regarding differences should be conservative or nonconservative. The most powerful tests (LSD and Duncan's) are nonconservative (ie, more likely to detect a significant difference when it doesn't exist). Scheff's S method is so conservative that it is not useful when pairwise comparisons are desired and is more appropriate for "data dredging," that is, looking at contrasts suggested by the data. Waller and Duncan have proposed a k ratio rule to determine whether one needs to use a conservative rule (such as Tukey's) or a nonconservative rule (such as Fisher's LSD). In practice, the SNK procedure is commonly used because it is a good compromise between power and conservatism.
TL;DR: Two recently developed probabilistic multidimensional models for analyzing pairwise choice data are introduced, discussed in terms of their differential properties, and extended in several ways.
Abstract: Two recently developed probabilistic multidimensional models for analyzing pairwise choice data are introduced, discussed in terms of their differential properties, and extended in several ways. The first one, the wandering vector model, was originally suggested by Carroll [12] and extended by De Soete and Carroll [30]. The second model, called the wandering ideal point model, is a more recently proposed [32] unfolding analog of the wandering vector model. A general maximum likelihood estimation method for fitting the various models described is mentioned, as well as a statistical test for assessing the goodness of fit. Finally, an application of the models is provided concerning consumer choice for some 14 brands of over-the-counter analgesics to illustrate how such models can be gainfully utilized for marketing decision making concerning product positioning.
01 Jan 1990
TL;DR: The findings of this paper reveal that although some methods appear to be more effective than others, still their performance is dramatically poor.
Abstract: One of the fundamental concepts in fuzzy set theory is the one of membership values. An appealing procedure for deriving information about membership values, is to use a matrix of pairwise comparisons [18], [19], [20]. A number of OR approaches that are based on eigenvalue theory and mathematical programming have been proposed to manipulate the previous matrices and estimate membership values. The findings of this paper reveal that although some methods appear to be more effective than others, still their performance is dramatically poor.
TL;DR: This work has shown that for a probabilistic Chooser, there is a significant likelihood that the subject might yield transitive pairwise preferences substantially different than the results suggested by May's model.
Abstract: May's model of pairwise preference determination is used to assess the expected likelihood that a subject's pairwise preference comparisons on three alternatives will be transitive. A closed form representation for this expected likelihood is obtained for each situation considered. When the subject is assumed to act precisely according to rankings on attributes with May's model, the computed expected likelihoods the relatively large. When the subject becomes a probabilistic chooser, as defined in a specific manner, expected likelihoods of transitivity decrease significantly from corresponding values with May's model. For a probabilistic Chooser, there is a significant likelihood that the subject might yield transitive pairwise preferences substantially different than the results suggested by May's model.
TL;DR: In this article, a new multicriteria decision aid, QualScal, is applied to the problem of selecting an extramural Fisheries R&D portfolio in the Ministry of Agriculture, Fisheries and Food.
Abstract: A new multicriteria decision aid, QualScal, is applied to the problem of selecting an extramural Fisheries R&D portfolio in the Ministry of Agriculture, Fisheries and Food. QualScal has been developed for the situation where the characteristics of the decision alternatives cannot be readily quantified. The decision-maker is only required to state either indifference or preference for each pair of the alternatives. A map representing the preference structure of the decision maker is produced with the aid of an enhanced version of the traditional nonmetric multidimensional scaling procedure, capable of scaling disjoint subsets of alternatives. Averaged results for the group of decision-makers facilitate a discussion to determine a mutually acceptable portfolio.
TL;DR: This paper examined the expected likelihood with which subjects will have transitive responses, as the degree of precision is varied, in a probabilistic choice model variation of May's model, in which subjects respond with various degrees of precision in comparison to the original algebraic choice model.
Abstract: May [18] developed an algebraic choice model of pairwise preference comparison in which subjects respond precisely to ordinal information on attributes of comparison. This study considers a probabilistic choice model variation of May's model, in which subjects respond with various degrees of precision in comparison to May's model. This precision can be viewed as an indirect measure of the subject's level of perception of the attributes of comparison. The purpose of the study is to examine the expected likelihood with which subjects will have transitive responses, as the degree of precision is varied. Closed form representations are obtained for the expected likelihood of transitivity for three alternatives for each different level of precision. Results indicate that a relatively small change in this precision can lead to substantial changes in the expected likelihood of transitivity.
TL;DR: A modified chi-squared test that involves multiple recalculations based on reiterative regrouping of the dataset is proposed, which evades problems caused by defining classes from an arbitrary starting point, but also avoids classes with too small an expected membership.
01 Jan 1990
TL;DR: The Analytic Hierarchy Process (AHP) is a mathematical technique to assist decision-makers in analyzing a problem that has been structured in a hierarchy of goals, criteria and alternatives as mentioned in this paper.
Abstract: The Analytic Hierarchy Process (AHP) is a mathematical (logical) technique to assist decision-makers in analyzing a problem that has been structured in a hierarchy of goals, criteria and alternatives. We have used AHP to structure the problem of choosing one or more recreational survey methodologies to estimate the weekly and seasonal recreational catch of striped bass, given temporal and statistical constraints. Each survey method or combination of methodologies has associated benefits and costs in terms of the defined criteria. Each alternative solution (survey method) is ranked in a pairwise comparison with all other alternatives according to the degree that it meets the requirements of each weighted criterion. It follows that the rankings associated with a criterion of low relative value will have a small effect on the overall conclusion. The conclusion comprises a list of alternatives (survey methods) with an associated value. The alternative with the highest value is the alternative that, relative to other listed alternatives, best satisfies the goal.
TL;DR: In a model of successive pairwise overlap, two parameter estimators for the expectation of underlying random variables are considered based on sample means having a tridiagonal covariance matrix, interested in the behavior of the relative efficiency as a function of certain problem parameters.
TL;DR: In this article, the Dayton-Morrill model was used to estimate palatability of certain bird foods in pairwise presentations, but the model relied solely on pairwise consumption totals as the response variable.
01 Jan 1990
TL;DR: In this article, the authors propose an approach to resolve the conflicts in which more than two parties are allowed to participate in the negotiation process and the trade-offs of benefits and costs are subsequently converted into numerical values on a discrete geometric scale.
Abstract: In this paper we propose an approach to resolve the conflicts in which more thantwo parties are allowable.It is a refinement and extension of Lootsma’s pairwise comparisonmethod for resolution of conflicts.The trade-offs of benefits and costs are judged in verbalterms which are subsequently converted into numerical values on a discrete geometric scale.Three schemes are suggested for supporting a mediator to recommend an appropriate dealto all the parties.We also present a procedure to estimate the trade-offs of the compositedeals.The approach is illustrated via the example of a market scramble.
TL;DR: This work has shown that 0.430 is the minimumBernoulli probability for which pairwise enabling is an optimal group testing algorithm under a Bernoulli arrival sequence model.
Abstract: Let p/sup 0/ be the minimum Bernoulli probability for which pairwise enabling is an optimal group testing algorithm under a Bernoulli arrival sequence model. In a previous work, it was shown that 0.430 >
TL;DR: Pairwise equilibria are studied in the context of voting models where candidates may be uncertain about voters' choices — and, therefore, may have expectations about those choices that are not deterministic.
TL;DR: A methodology is proposed for transforming rank ordered data into pairwise comparison matrices, so that AHP can be used for measuring consumer preferences.
Abstract: It is clearly not enough in product research to show that people prefer one product to another, but one must also show what attributes of the product cause them to prefer it. Saaty′s Analytic Hierarchy Process (AHP) is an appropriate method for measuring and analysing multidimensional attributes for design and redesign considerations. However, it is not reasonable to expect that consumers are able and willing pairwise to compare attributes, as Saaty′s method assumes. A methodology is proposed for transforming rank ordered data into pairwise comparison matrices, so that AHP can be used for measuring consumer preferences. The methodology is applied to the design of milk containers.
TL;DR: Properties and relationships of some commonly used probability bounds, along with other recently developed bounds and approximations, are evaluated for their performance with pairwise comparisons.
Abstract: Properties and relationships of some commonly used probability bounds, along with other recently developed bounds and approximations, are evaluated for their performance with pairwise comparisons. The comparisons are of independent sample means obtained from normal random variables with a common variance. Computational methods are presented and numerical results are used to further evaluate the performance of the bounds.
TL;DR: In this paper, a minimum-cost network-flow problem is presented in conjunction with a sensitivity diagnostic that assesses the influence of a single pairwise comparison on traditional Thurstone (ordinary least squares) scale estimates.
Abstract: This paper presents an approach for determining unidimensional scale estimates that are relatively insensitive to limited inconsistencies in paired comparisons data. The solution procedure, shown to be a minimum-cost network-flow problem, is presented in conjunction with a sensitivity diagnostic that assesses the influence of a single pairwise comparison on traditional Thurstone (ordinary least squares) scale estimates. When the diagnostic indicates some source of distortion in the data, the network technique appears to be more successful than Thurstone scaling in preserving the interval scale properties of the estimates.
TL;DR: This paper presents a method to reduce the number of pairwise comparison at each level of the decision hierarchy in an altanatives evaluation model for interactive computer systems.
Abstract: It is necesarry to support planners evaluating altanative plans scientificaly and efficiently. We discuss an altanatives evaluation model for interactive computer systems. The analytic hierarchy prosess (AHP) is a convenient decision analysis technique. However, realistic decision problems usually involves large number of pairwise comparison at each level of the decision hierarchy. As the number of judgements increases, the estimated weights can be expected to be less reliable. This paper presents a method to reduce the number of pairwise comparison.